1. Field of the Invention
The present invention relates to a lamp having an illuminant section, for reflecting and condensing light emitted from an illuminant within the range of a radiation angle, and relates to a condensing optical system and an image display device which use the lamp.
2. Description of the Related Art
FIG. 1 is a diagram showing a configuration of a condensing optical system using a conventional lamp and showing a sectional view of the condensing optical system which has been cut by a plane including the optical axis of the optical system.
In FIG. 1, reference number 101 designates the conventional lamp, 101a denotes an illuminant, 101b indicates a lamp reflector, and 101c designates a lamp front glass.
The conventional lamp 101 is made up of the illuminant 101a, the lamp reflector 101b, and the lamp front glass 101c. 
The illuminant 101a has a glass bulb and electrodes placed at the center of the bulb. The light is generated in and emitted from a space between the electrodes. The space between the electrodes is a light source of the illuminant 101a. 
The lamp reflector 101b is a reflecting mirror formed on an ellipsoid of revolution, in which the illuminant 101a is located at one of two foci of the ellipsoid of revolution (hereinafter referred to as “parabolic focus”) and at the center position between the electrodes. The ellipsoid of revolution reflects the light emitted from the illuminant 101a. 
The ellipsoid of revolution means a space curved surface obtained by rotating a part of the ellipsoidal around its rotation major axis (or optical axis)
When light emitted from one of the foci of the ellipsoidal surface on the optical axis is reflected by the ellipsoid of revolution, it is well known that all of the reflected light is condensed into the other focus of the ellipsoidal. That is, the two of the ellipsoidal are conjugate points.
The use of this principle can make the lamp have a condenser function. When compared with the lamp using the paraboloid of revolution generating parallel light, the lamp 101 can be constructed with a small number of components because the ellipsoid of revolution condenses light and it thereby does not require any condenser lens for condensing parallel light into the lens focus.
Based on the above reasons, in the lamp 101 the illuminant 101a is an approximate point light source, and the center point of the electrodes of the illuminant 101a is coincided with one focus of the ellipsoid of revolution of the lamp reflector 101b, and the lights emitted from the illuminant 101a are reflected by the lamp reflector 101b and then condensed into the other focus of the ellipsoid of revolution.
The lamp front glass 101c is so placed that it covers an aperture of the lamp reflector 101b. This prevents the occurrence of a rarely accident caused by explosion of the illuminant 101a, so that the lamp front glass 101c can prevent to spread the damage of the explosion to other optical elements.
The lights, of course, reflected by the lamp reflector 101b are radiated to external section of the lamp 101 through the lamp front glass 101c. In the conventional lamp 101, it is so designed that the incident plane (or incoming plane) and the outgoing plane of the lamp front glass 101c are planes which go straight to the optical axis Z, so that the incident plane and the outgoing plate of the lamp front glass 101c refract the lights from the lamp reflector 101b and condense the lights into the focus on the optical axis apart from the other focus of the ellipsoid of revolution.
Reference 103 designates a column-shaped glass called “a rod integrator” having a configuration in which the light is input through its incident plane and transmitted through the inside of the rod integrator and output through its outgoing plane. In order to increase the light receiving efficiency at the incident plane and to suppress a loss as low as possible by increasing the amount of the incident light as large as possible, the incident plane of the rod integrator 103 is placed at the condenser point of the light passed through the lamp front glass 10c. 
The line Z through which the center of the illuminant 101a and the center of the incident plane of the rod integrator 103 are connected is a common optical axis. The positive direction (or forward direction) of the optical axis Z is a forward direction of the light. The space near the optical axis Z indicated by reference character D is a dead zone where there is no light flux. The conventional condensing optical system comprises the lamp 101, the condenser lenses 102a and 102b, and the rod integrator 103.
Before the explanation of the operation of the condensing optical system shown in FIG. 1, a description will now be given of the explanation of a brilliance distribution characteristic and an orientation distribution characteristic of the illuminant 101a. 
FIG. 2 is a diagram showing a typical brilliance distribution characteristic of the illuminant 101a. For example, the illuminant 101a such as a metal halide lamp and a high pressure mercury lamp has the brilliance distribution characteristic shown in FIG. 2.
In FIG. 2, reference characters 101d and 101e denote the electrodes of the illuminant 101a, Pd and Pe indicate emitting front points closed to the electrodes 101d and 101e, and Pf designates the center point of the emitting front points Pd and Pe.
As previously explained, the center point Pf is equal in position to the ellipsoidal focus of the lamp reflector 101b. Reference number 104 designates the brilliance distribution of the illuminant 101a shown in contour lines. The brilliance distribution 104 is shown using the relatively brilliance values 10–90 every 10.
The distance d shown in FIG. 2 is called an arc length that is one of indexes of the performance of the lamp 101. That is, the arc length d is an approximation parameter indicating the degree of the similarity between the actual illuminant 101a and an ideal point light source.
When the magnitude of the arc length d is smaller as low as possible, the front points Pd and Pe of the electrodes 101d and 101e become closer to the center point Pf, so that the illuminant 101a becomes closer to the ideal point light source.
Thus, the illuminant 101a has the illuminant of a finite size defined by the arc length d. When AC or DC voltage is applied to the electrodes 101d and 101e, the light is emitted from the space between the electrodes 101d and 101e according to the brilliance distribution 104. As can be understood from FIG. 2, the maximum brilliance of a relative brilliance value of approximately 90 is obtained at the front points Pd and Pe of the electrode 101d and 101e. The relative brilliance value 50–60, which is slightly smaller than the maximum brilliance value, is obtained at the center point Pf. The relative brilliance value is gradually decreased to the value 10 according to increasing of the distance from the front points Pd and Pe.
Thus, the point where the maximum brilliance value is obtained is the front point Pd or Pe which is shifted from the center point Pf by half of the arc length d. That is, the brilliance value obtained at the center point Pf, namely at the ellipsoidal surface focus of the lamp reflector 101b is not the maximum brilliance value.
FIG. 3 is a diagram showing the orientation distribution characteristic of the illuminant 101a, where reference number 105 indicates an orientation distribution. In FIG. 3, the center point Pf of the illuminant 101a is the orientation O, and the forward direction of the optical axis Z is defined as the radiation angle of zero, and the clockwise direction on a sheet is the direction from zero to 360 degrees. In FIG. 3, a luminous intensity is indicated every 20 degrees from zero to 100 around the origin O in direction of a constant radiation angle. In this case, for example, a point farther from the origin O has a higher luminous intensity and the luminous intensity of the origin O is zero. When the luminous intensity is measured on an optional plane including the optical axis z shown in FIG. 1, the orientation distribution shown in FIG. 3 is obtained.
The orientation distribution 105 shows the higher luminous intensity of not less than 80 at two ranges of the radiation angles 60–120 and 240–300. On the other hand, the orientation distribution 105 shows the lower intensity of light at two ranges of angles of approximately ±50 around the radiation angle zero and around the radiation angle 180. This means that the electrodes 101a and 101b are placed in the illuminant 101a, and the light is cut by shadows of the electrodes 101d and 101e at approximately ±50 around zero and around 180, as shown in FIG. 2.
A description will be given of the operation of the condensing optical system shown in FIG. 1.
The greater part of light emitted from the illuminant 101a is reflected by the lamp reflector 101b. As shown in FIG. 2, because the illuminant 101a has the luminous of a finite size designated by the arc length d, the reflected lights from the lamp reflector 101b become an imperfect light flux to be transmitted to the other focus point of the ellipsoidal. This light flux goes toward the forward direction of the optical axis Z through the lamp front glass 101c. As has been previously described regarding the orientation distribution characteristic shown in FIG. 3, the dead zone D is present where there is no light because of the shadow of the electrodes 101d and 101e. 
The light flux from the lamp 101 is condensed to the lens focus on the optical axis Z after refracting it by the incident plane and the outgoing plane of the lamp front lens 101c. The condensed light flux is then input into the incident plane of the rod integrator 103, and transmitted through the inside of the rod integrator 103, as shown in following FIG. 4.
FIG. 4 is a diagram showing an optical path of the transmitted light through the inside of the rod integrator 103. In FIG. 4, reference characters 103a, 103b, and 103c designate the incident plane, the side surface, and the outgoing plane of the rod integrator 103, respectively. Both the incident plane 103a and the outgoing plane 103b are perpendicularly intersected to the optical axis Z.
The lamp front glass 101c is so designed that the incident lights input into the incident plane 103a are transmitted while performing the total reflection at the side surface 103b of the rod integrator 103. Therefore, the incident lights through the incident plane 103a are totally reflected repeatedly at the side surface 103b and finally output through the outgoing plane 103c. Because the rod integrator 103 uses the phenomenon of the total reflection, there is no leaking of light through the side surface 103b and no loss in the rod integrator 103.
At this time, because the lights from the lamp front glass 101c are input into the incident plane 103a at various incident angles, an illumination distribution of the lights after performing the total reflection repeatedly at the side surface 103b becomes approximately uniform at the outgoing plane 103c. 
FIG. 5A and FIG. 5B are diagrams showing the illumination distribution characteristic of the incident light and the outgoing light of the rod integrator 103. In FIGS. 5A and 5B, an axis parallel to the optical axis Z shows the illumination of the incident light and the outgoing light.
The rod integrator 103 has the function to convert the incident light having the illumination distribution like Gauss distribution (see FIG. 5A) into the outgoing light having a uniform illumination distribution (see FIG. 5B).
The lights of the uniform illumination distribution made by the rod integrator 103 are transferred by the following optical system. For example, in cases of an image display device using an optical modulation element such as a DMD chip (Digital Micro mirror Device which is a trade mark of Texas Instrument Incorporated (TI)) or a crystal liquid panel, the outgoing lights from the rod integrator 103 are irradiated to the optical modulation element through a relay optical system in order to obtain image information. The lights with the image information are projected onto a screen through a projecting optical system, so that the image based on the image information is displayed on the screen.
Because of the configuration described above, the conventional lamp involves a drawback to increase the divergent angle of the outgoing light flux after the lamp reflector reflects the lights from the illuminant.
Further, because of the configuration described above, the conventional condensing optical system involves a drawback to spread the illuminant image at the focus point of the lamp front glass and thereby to cause a leaking loss of the incident lights at the incident plane of the rod integrator.
Furthermore, because of the configuration described above, the conventional image display device described above involves a drawback to decreases the brightness of the image to be projected on the screen by the leaking loss generated at the incident plane of the rod integrator.
A description will now be given of the explanation for each of the above conventional drawbacks.
In FIG. 1, when the illuminant 101a is an ideal point light source in geometry, lights emitted from the illuminant 101a are transmitted to the other focus of the ellipsoidal by the reflection of the lamp reflector 101b. Thus, because all of the lights are condensing to the condensing point at the lamp reflector 101b and then transmitted into the incident plane 103a of the rod integrator 103, there is no leaking loss of the lights caused at the incident plane 103a excepting a reflection loss in the lamp reflector 101b and the like.
However, as has been explained using FIG. 2, because the illuminant 101a has a light source of a finite size defined by the arc length d, it is not the ideal point light source. Accordingly, the illuminant image having a finites size is generated at the incident plane of the rod integrator 103 because the light distribution at the incident plane 103a of the rod integrator 103 is not condensed into the condensing point.
FIG. 6 is a diagram showing the explanation for the image of the illuminant 101a appeared at the incident plane 103a of the rod integrator 103.
In FIG. 6, the center point Pf is selected as a reference point. This center point Pf is equal to the front points Pd and Pe having the maximum brilliance and the one focus of the ellipsoidal shown in FIG. 2. FIG. 6 shows the state to condense the lights 106d and 106e, and 106f transmitted from those points Pd, Pe, and Pf into the incident plane 103a. 
In this case, we will pay an attention to both the point 101z on the outgoing plane of the lamp front glass 101c and the lights passing through this point 101z. 
Accordingly, the light 106f is input into the incident plane 103a based on the design without any leaking of the incident lights.
On the other hand, because the points Pd and Pe at which the lights are generated are not on the other focus of the ellipsoidal, the lights 106d and 106e passing through the point 101z in the light flux from the front points Pd and Pe are not condensed into the other focus of the ellipsoidal after the reflection by the lamp reflector 101b. That is, the lights emitted from the point 101z in the lamp front glass 101 are not transmitted into the condensing point.
In this case, when the lamp front glass 101c is recognized as a virtual plane light source, it is defined that this light source generates lights having the maximum divergent angle at the point 101z around the light 106f as the center, such as the lights 106d and 106e. 
Because the inclined lights 106d and 106e have an angle which is out of the design, when the lights are condensed into the incident plane 103a by the lamp front glass 10c, many of the lights are out of the sectional area of the incident plane 103a. 
In this case, the lights generated at each point between the electrodes 101d and 101e around the center point Pf do not become the complete point at the condensing point after transmitting through the lamp front lens 10c. This forms an illuminant image whose size is larger in area than the sectional area of the incident plane 103a. 
FIG. 7 is a diagram showing the result of quantitative analysis of the receiving of the lights 106d, 106e, and 106f at the incident plane 103a. FIG. 7 is a diagram showing the relationship between the outgoing position of the outgoing light from the lamp front glass 101c and the incident position of the incident light to the incident plane 103a. 
In FIG. 7, the horizontal axis represents the position through which the light is output from the lamp front glass 10c, which has a distance R measured from the optical axis Z show in FIG. 6. The vertical axis designates the position through which the light is input into the incident plane 103a, which has a distance Ri measured from the optical axis Z shown in FIG. 6.
In this analysis, the lamp 101 has the arc length d=1.1 [mm], the aperture diameter 40 [mm] of the lamp reflector 101b, and the sectional area 3.8×5.5 [mm2] of the incident plane 103a. The lamp front lens 101c focus the light to the incident plane 103a with F value=1.
The line Ri=±1.9 [mm] indicated by the reference characters 107a and 107b shown in FIG. 7 represents the boundary of the incident plane 103a and the region |Ri|≦1.9 [mm] corresponds to the size of the incident plane 103a. 
Because the incident position of the light 106f to the total outgoing range of R=0–11 [mm] becomes |Ri|<approximately 0 [mm], it is understood that the light 106f is always input into the incident plane 103a. 
In addition, the lights 106d and 106e are in the boundary 107a–107b of the incident plane 103a within the outgoing range of R=approximately 7–11 [mm] which is greatly apart from the output axis Z. Therefore no leaking of the input light occurs within the outgoing range, and there occurs no loss of the leaking light.
On the contrary, the lights 106d and 106e are out of the boundary 107a–107b in the outgoing range relatively close to the optical axis Z of not more than R=approximately 7 [mm]. That is, the loss Ld of the light 106d occurs within the outgoing range of R=approximately 0–4.5 [mm], and the loss Le of the light 106e occurs within the outgoing range of R=approximately 2–7 [mm].
This case includes a serious problem that the luminous intensity in the losses Ld and Le are greater than that in other areas. The reason will now be explained with reference to FIG. 8. FIG. 8 is a diagram showing the luminous intensity distribution of the outgoing light from the lamp front glass 101c. Similar to the case shown in FIG. 7, the horizontal axis indicates the distance R measured from the optical axis and the vertical axis represents the relative luminous intensity (Illumination×a very short ring-shaped area) of the outgoing light.
As clearly understood from FIG. 8, for example, the range of the outgoing light having the relative luminous intensity of approximately not less than approximately 0.1 is R=approximately 4–7.5 [mm].
It can be understood that the volume zone V having the large luminous intensity of the lamp 101 nearly corresponds to the outgoing ranges R=approximately 0–4.5 [mm] and R=approximately 2–7 [mm] of the losses Ld and Le previously shown. That is, the light in the volume zone V having the maximum luminous intensity can not be input to the incident plane 103a, namely, this light becomes a loss.
In order to solve the above problems, it can be recognized to enlarge the size of the incident plane 103a. However, considering a viewpoint of the yield rate of the manufacture, it is quite advantageous to use photo modulation elements such as DMD chips and liquid crystal panels have a small incident area to input lights. Further, because the size of the incident plane 103a of the rod integrator 103 becomes small in proportional to the size of the photo modulation element from a view point of magnification of lenses, the above method cannot easily solve this problem.